A New Approach to Deriving Interatomic Many-Body Interactions in Metals

Abstract

An original method of treating the kinetic and exchange-correlation energies functionals in terms of many particle interactions was developed. It is based on utilizing the local density approximation. The total electron density, extracted from the ab initio .band structure calculations, is expressed as a linear superposition of contributions from the individual pseudoions embedded in the uniform background. The explicit expressions for the pair and triplet potentials are presented. The general form for the part of the pair interatomic interactions caused by the kinetic and. the exchange-correlation effects is obtained. Relationship between the developing approach and the perturbation theory in pseudopotential is analysed. Unlike the perturbation theory the advanced approach allows one to calculate accurately the so-called reducible contributions to the pair potential arising from the n-particle (n > 2) inter-. actions. It corresponds to summing certain series in pseudopotential. Contribution of the electron-nonlocal pseudopotential interactions to the pair interatomic ones is considered within the concept of the fully separable pseudopotentials.

Ab Initio Derivation of Interatomic Interactions in Transition Metals

“…For explicit expressions for t(ρ σ (r)) see [1,9]. As will be shown in the next section, utilizing approximations (i) and (ii) allows one to develop the total energy of TM as a multi-ion interaction expansion…”

“…The electron density ρ(r), (2.1), as well as the functions ε 0 xc (ρ σ (r)) and t(ρ σ (r)) in (2.5) and (2.6) are periodical because of the crystal periodicity. Therefore, one should consider (2.5) and (2.6) in the region of the unit cell only [1,5]. The valence electron density ρ σ (r), extracted from the ab initio band structure calculations, can be represented in the unit cell region as follows…”

“…The kinetic energy functional is treated in terms of contributions to the indirect interatomic potentials in a similar way [1,5]. Then, using (3.1) to (3.7) and (2.5), (2.6), one can represent the sum…”

“…It is caused by utilizing these potentials in many physical and material problems. The first-principles and the (semi)empirical methods are the two approaches which dominate this field at present (see review of literature in [1]). In some cases, an adequate theoretical description of metal and alloy properties could not be achieved within the pair interatomic interaction model.…”

“…The subject of the present paper is to get these potentials for the case when the spin orientation is included into consideration explicitly. The method proposed in [1,5] for simple metals is generalized here for TM.…”